Global Bifurcation and Highest Waves on Water of Finite Depth
(2023) In Archive for Rational Mechanics and Analysis 247.- Abstract
We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 ∘ . In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the... (More)
We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 ∘ . In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity.
(Less)
- author
- Kozlov, Vladimir and Lokharu, Evgeniy LU
- organization
- publishing date
- 2023-10
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Archive for Rational Mechanics and Analysis
- volume
- 247
- article number
- 98
- pages
- 30 pages
- publisher
- Springer
- external identifiers
-
- scopus:85171881063
- ISSN
- 0003-9527
- DOI
- 10.1007/s00205-023-01929-x
- language
- English
- LU publication?
- no
- additional info
- Funding Information: V.K. was supported by the Swedish Research Council (VR), 2017-03837. Publisher Copyright: © 2023, The Author(s).
- id
- 4b7bcb0e-3c12-4a2a-972b-fc53961fd001
- date added to LUP
- 2023-11-03 13:18:23
- date last changed
- 2023-11-07 12:04:05
@article{4b7bcb0e-3c12-4a2a-972b-fc53961fd001,
abstract = {{<p>We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 <sup>∘</sup> . In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity.</p>}},
author = {{Kozlov, Vladimir and Lokharu, Evgeniy}},
issn = {{0003-9527}},
language = {{eng}},
publisher = {{Springer}},
series = {{Archive for Rational Mechanics and Analysis}},
title = {{Global Bifurcation and Highest Waves on Water of Finite Depth}},
url = {{http://dx.doi.org/10.1007/s00205-023-01929-x}},
doi = {{10.1007/s00205-023-01929-x}},
volume = {{247}},
year = {{2023}},
}